Two bodies $A$ and $B$ start from rest from the same point with a uniform acceleration of $2\,m/s^2$. If $B$ starts one second later,then the two bodies are separated,at the end of the next second,by $.............\,m$.

$A$ body starts from rest with an acceleration of $8\,m/s^2$. What distance will it cover in the $5^{th}$ second?

$A$ particle moves a distance $x$ in time $t$ according to the equation $x = (t + 5)^{-1}$. The acceleration of the particle is proportional to:

If the decrease in velocity is the same in equal intervals of time,then describe the $x-t$ graph.

$A$ particle executes the motion described by $x(t) = x_0 (1 - e^{-\gamma t})$ for $t \geqslant 0$ and $x_0 > 0$.
$(a)$ Where does the particle start and with what velocity?
$(b)$ Find the maximum and minimum values of $x(t)$,$v(t)$,and $a(t)$. Show that $x(t)$ increases with time,$v(t)$ decreases with time,and $a(t)$ increases with time.

$A$ body is moving with a uniform acceleration covers $40\,m$ in the first $4\,s$ and $120\,m$ in next $4\,s.$ Its initial velocity and acceleration are